# Particle Filters for Partially-Observed Boolean Dynamical Systems

## TL;DR

This paper develops particle filter-based algorithms for estimating states and parameters in partially-observed Boolean dynamical systems, enabling scalable analysis of complex Boolean processes like gene regulatory networks from noisy data.

## Contribution

It introduces approximate MMSE filtering and smoothing algorithms using auxiliary particle filters for large POBDS, along with a specialized EM-based smoother for parameter estimation.

## Key findings

- Algorithms successfully applied to gene regulatory network data
- Improved computational efficiency over exact methods
- Effective state and parameter estimation demonstrated

## Abstract

Partially-observed Boolean dynamical systems (POBDS) are a general class of nonlinear models with application in estimation and control of Boolean processes based on noisy and incomplete measurements. The optimal minimum mean square error (MMSE) algorithms for POBDS state estimation, namely, the Boolean Kalman filter (BKF) and Boolean Kalman smoother (BKS), are intractable in the case of large systems, due to computational and memory requirements. To address this, we propose approximate MMSE filtering and smoothing algorithms based on the auxiliary particle filter (APF) method from sequential Monte-Carlo theory. These algorithms are used jointly with maximum-likelihood (ML) methods for simultaneous state and parameter estimation in POBDS models. In the presence of continuous parameters, ML estimation is performed using the expectation-maximization (EM) algorithm; we develop for this purpose a special smoother which reduces the computational complexity of the EM algorithm. The resulting particle-based adaptive filter is applied to a POBDS model of Boolean gene regulatory networks observed through noisy RNA-Seq time series data, and performance is assessed through a series of numerical experiments using the well-known cell cycle gene regulatory model.